Title : Optimal Allocations in the Construction of k-Out-of-n Reliability Systems.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH

Personal Author(s) : Derman,C. ; Lieberman,G. J. ; Ross,S. M.

Report Date : 17 SEP 1973

Pagination or Media Count : 25

Abstract : The authors want to build n components so as to form an n component system which will function if at least k of the components function. If x dollars is invested in building a component then this component will function with probability P(x), where P(x) is an increasing function such that P(O) = O. The problem of interest is to determine how much money should be invested in each component so as to maximize the probability of attaining a functioning system. The authors are interested in this problem both in the sequential and in the nonsequential case. Section 2 considers the case k = 1. Conditions are presented on P(x) under which (a) it is optimal to put an equal investment in all n components and (b) it is optimal to put the total fortune A into a single component. In Section 3, it is shown that the equal investment condition carries over to the case of general k. In Section 4 the special case P(X) = x in the sequential situation is considered and the optimal policy is determined when k = 2. A conjecture as to the optimal policy in the general case is also made. Several remarks are made concerning the non-sequential case with P(x) = x in Section 5. In the final section a related problem is considered. (Modified author abstract)